Monday, February 18, 2019

Friday, February 15, 2019

The Lunar Smoking Gun


Wilson and Sidorenkov, A Luni-Solar Connection to Weather and Climate I: Centennial Times Scales, J Earth Sci Clim Change 2018, 9:2 DOI: 10.4172/2157-7617.1000446

https://www.omicsonline.org/open-access/a-lunisolar-connection-to-weather-and-climate-i-centennial-times-scales-2157-7617-1000446.pdf


When a plot is made of the precision of these [lunar] alignments, in a frame-of-reference that is fixed with respect to the Perihelion of the Earth’s orbit, the most precise alignments take place in an orderly pattern that repeats itself once every 208.0 years: 

0 × (28.75 + 31.00) + 28.75 years = 28.75 years ≈ 25.5 FMC’s 
1 × (28.75 + 31.00) + 28.75 years = 88.5 years ≈ 78.5 FMC’s 
2 × (28.75 + 31.00) + 28.75 years = 148.25 years ≈ 131.5 FMC’s 
3 × (28.75 + 31.00) + 28.75 years = 208.0 years ≈ 184.5 FMC’s 

A simple extension of this pattern gives additional precise alignments at periods of 236.75, 296.50, 356.25, 416.0, 444.75 and 504.5 years. The full significance of the 208-year repetition pattern in the periodicities of the lunar alignment index (ϕ) only becomes apparent when these periodicities are compared to those observed in the spectra for two proxy time series. 

Abstract 

Lunar ephemeris data is used to find the times when the Perigee of the lunar orbit points directly toward or away from the Sun, at times when the Earth is located at one of its solstices or equinoxes, for the period from 1993 to 2528 A.D. The precision of these lunar alignments is expressed in the form of a lunar alignment index (ϕ). When a plot is made of ϕ, in a frame-of-reference that is fixed with respect to the Perihelion of the Earth’s orbit, distinct periodicities are seen at 28.75, 31.0, 88.5 (Gleissberg Cycle), 148.25, and 208.0 years (de Vries Cycle). The full significance of the 208.0-year repetition pattern in ϕ only becomes apparent when these periodicities are compared to those observed in the spectra for two proxy time series. The first is the amplitude spectrum of the maximum daytime temperatures (Tm) on the Southern Colorado Plateau for the period from 266 BC to 1997 AD. The second is the Fourier spectrum of the solar modulation potential (ϕm) over the last 9400 years. A comparison between these three spectra shows that of the nine most prominent periods seen in ϕ, eight have matching peaks in the spectrum of ϕm, and seven have matching peaks in the spectrum of Tm. This strongly supports the contention that all three of these phenomena are related to one another. A heuristic Luni-Solar climate model is developed in order to explain the connections between ϕ, Tm and ϕm. 

Monday, February 11, 2019

The Lunar Tidal Model - Part 4


Please read:

The Lunar Tidal Model - Part 1
http://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-1.html

The Lunar Tidal Model - Part 2
https://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-2.html



The Lunar Tidal Model - Part 3
http://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-3.html

Introduction

An MJO is a complex atmospheric wave that moves from west-to-east along the equator. It is most evident when it couples with atmospheric convection/precipitation between East Africa and the equatorial Western Pacific Ocean. It consists of an active region of enhanced precipitation/uplift followed by a region of suppressed precipitation. The precipitation pattern takes about 30 – 60 days to complete one cycle when seen from a given point along the equator.

The slow-moving MJO wave can be thought of as a combination of an easterly moving Kelvin-wave and a westerly moving equatorial Rossby wave. The compound MJO wave moves with a group velocity of about 5 m/sec from west-to-east. Within the large MJO wave train, Kelvin waves move from west-to-east with a phase velocity of 15 to 20 m/sec, and the equatorial Rossby Waves travel from east-to-west with a phase velocity of 5 m/sec.


Figure 1


Equatorial Rossby Waves (ERW)

In parts 1, 2, and 3, it was shown that the westward-moving ERWs trailing the active phase of the MJO are being generated at the times when there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator [when measured at the same time in the 24.8-hour lunar tidal day], i.e. either at a tidal minimum (at a lunar standstill) or at a tidal maximum at the Earth's equator (at a lunar equatorial crossing).

Figure 2 reminds us that these ebbs in the lunar-induced atmospheric/oceanic tides at the Earth's equator occur roughly every 6-7 days, either when the peak of the Moon's tidal bulge crosses the Earth's equator (tidal maximum) or when it reaches its maximum distance from the Earth's equator i.e. lunar standstill (tidal minimum).


Figure 2




Equatorial Kelvin Waves (EKW)


The MJO can be thought of as a combination of an easterly moving EKW and a westerly moving ERW with the compound MJO wave moving with a group velocity of about 5 m/sec from west-to-east. Within the larger MJO wave train, Kelvin waves move from west-to-east traveling through MJO with a phase velocity of 12 to 20 m/sec. Specifically, the phase velocity of an EKW is typically 15 — 20 m/sec (west-to-east) over the western Pacific Ocean and 12 — 15 m/sec (west-to-east) over the Indian Ocean. In addition, EKWs are non-dispersive waves, so their phase velocity is equal to their group velocity. Hence, their slower speed over the Indian Ocean is attributed to the fact that, in these regions, EKWs are coupled with the atmospheric convection and precipitation.

See Dr. Kyle MacRitchie's excellent blog site for further details:

If you were to observe the Moon from a fixed point on the Equator at the same time each day, you would notice that the sub-lunar point on the Earth's surface appears to move at a speed of 15 — 20 m/sec from west-to-east. This is the result of the fact that the west-to-east speed of the Moon along the Ecliptic (as seen from the Earth’s center) varies between 15.2 — 19.8 m/sec. 

Interestingly, the west-to-east group (and phase) velocity for the convectively-decoupled EKW in the western Pacific Ocean is 15 — 20 m/sec, as well. This remarkable "coincidence" leads to a very intriguing hypothesis (N.B. the following assumes that the observer is at a fixed location on the Earth's equator). 

Could it be that the easterly moving EKW that are embedded within the MJO wave complex is produced by the interaction between the day-to-day movement of the lunar-induced atmospheric/oceanic tides with a meteorological phenomenon that routinely occurs at roughly the same time each (24 hr) solar day? 

THE FIRST POSSIBILITY

The first meteorological phenomenon that comes to mind is the observation that in the tropics the peak in convective thunderstorm activity routinely takes place at roughly 3.00 p.m. each afternoon.

Hypothesis: EKWs are generated when the peak in the lunar-induced tides passes through the local meridian at 3:00 p.m. local time* when the daily thunderstorm activity reaches its peak (this takes place roughly once every half synodic month = 14.8 days)**. In addition, if the generation of an EKW occurs at roughly the same time as the generation of an ERW (which takes place roughly once every quarter of a Tropical month = 6.83 days)***, the combined atmospheric waves reinforce the Westerly Wind Bursts (WWBs) that are produced by ERWs.

Some important notes:

* The lunar-induced tidal peak can pass through the local meridian (during its daily passage) both when the Moon is passing through the meridian and when the Moon is passing through the anti-meridian due to the semi-diurnal nature of the peak tides.

** If you select times when the Moon passes through the local meridian at a fixed time (e.g. 3:00 p.m.), you are in fact selecting times when the Moon is at a specific phase (or a fixed point in the Synodic month). Hence, when the Moon is passing through the meridian at 3:00 p.m. for someone located in the equatorial Indian and western Pacific Oceans, the Moon's phase is at ~15 % (Waxing Crescent), and when the Moon is passing through the local anti-meridian it's at ~85 % (Waning Gibbous).

***There are four times where the Moon either crosses the equator or reaches a standstill in one Tropical month.

The main prediction of this hypothesis is that WWBs should be enhanced near the active phase of an MJO every time an ebb in the lunar-induced equatorial tides coincides with the time when the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m.

One way to test this prediction is to look at a Hovmoller diagram of Westerly Wind Burst anomalies (WWBanom). This should show that whenever there is a temporal alignment between the two generating mechanisms, there should be an increase in the WWBanom. 

Figure 3 below shows the Hovmeller diagram of the WWBanom (between +/- 15 degrees latitude) versus geographic longitude between January 1st, 2002 and December 31st, 2003. The starting and ending dates were chosen to cover the 2002/2003 El Nino event, which spans the period from May 2002 and February 2003.

Ref: Australian Bureau of Meteorology (BOM) - last accessed 12/02/2019.
http://www.bom.gov.au/climate/mjo/#tabs=Time-longitude 

The thick black horizontal lines that are superimposed on this plot show the 45 degrees East and 180 degrees East meridians. The former marks the western-most part of the Indian Ocean off the coast of East Africa and the later marks the location of the International Date-Line.

Large crosses are superimposed on figure 3, using:

a) the dates on which the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m (which are assumed to be responsible for the EKWs), at the same time as there is an ebb in the lunar-induced equatorial tides (which are assumed to be responsible for the ERWs).    

b) the longitude of the MJO phase for that date.

[Note: the following table is used to convert between MJO phase and longitude: Phase 1 = 60 deg. E; Phase 2 = 75 deg. E; Phase 3 = 90 deg. E; Phase 4 = 105 deg. E; Phase 5 = 120 deg. E; Phase 6 = 150 deg. E; Phase 7 = 170 deg. E; Phase 8 arbitrarily set to 120 deg. W.]

All of the points are plotted that have a difference between, the time when the peaks in the semi-diurnal tides pass through the local meridian at 3:00 p.m., and the time when there is an ebb in the lunar-induced equatorial tides, that is either -1, 0, or +1 days.    

Figure 3



Important Notes:

1. The passage of MJO events across the Indian and Western Pacific oceans in figure 3 are traced out by positive (purple) WWB anomalies. Hence, simply plotting a point in figure 3, using its MJO phase and its date, will automatically place that point along one of the purple paths traced out by the MJO event. Hence, what we are looking for in figure 3 is not whether the alignment points lie along the paths traced out by the MJO but whether or not these points are near noticeably enhanced periods of WWB anomalies in a given MJO event.

2. The points that have alignments of 0 or 1 days appear to lie in MJO phase regions 5, 6 or 8, at least over the one and half year period that is centered on the 2002/2003 El Nino event. 

[Note: information from a much longer time series extending from January 1996 to January 2019 shows that points that are not aligned (i.e. not 0 or 1 days) are not preferentially clustered in MJO phase regions 5 and 6.] 

3. The points that have alignments of 0 or 1 days and which are located in the MJO phase regions 5 and 6, appear to immediately precede noticeably enhanced periods of WWB anomalies by a couple of days. This appears to confirm the main prediction of our hypothesis.

4. There appear to be noticeably enhanced periods of WWB anomalies in MJO phase regions 5 and 6 that lie halfway in between the points that have alignments of 0 or 1 day.

Note 4. strongly suggests that our orginal hypothesis needs to be modified to allow for the possibility that the easterly moving EKW that are embedded within the MJO wave complex is produced by the interaction between the day-to-day movement of the lunar-induced atmospheric/oceanic tides with a meteorological phenomenon that not only occurs at around 3:00 p.m. local time but also 12 hours earlier around 3:00 a.m. local time.  

A MORE LIKELY POSSIBILITY 

One meteorological phenomenon that fits this bill is the atmospheric surface pressure variations measured at a given location in the tropics. At many points near the equator, the atmospheric surface pressure spends much of its time sinusoidally oscillating about its long-term mean with an amplitude of 1 to 2 hPa (or millibars). Generally, this regular daily oscillation is only disrupted by the passage of a tropical low-pressure cell.

Figure 4 shows the diurnal surface pressure variations in the Carribean as measured by Haurwitz (1947). What this shows is that like many points near the Earth's equator, the atmospheric surface pressure in the Carribean reaches a minimum near 4:00 -- 4:30 a.m. and 4:00 -- 4:30 p.m.

Figure 4.
Source; Figure 1 of Haurwitz B., 1947, Harmonic Analysis of the Diurnal Variations of Pressure and Temperature Aloft in the Eastern Caribbean, Bulletin of the American Meteorological Society, Vol. 28, pp. 319-323.  
This leads us to modify our original hypothesis so that it reads:

Modified Hypothesis: 

EKWs are generated when the peak in the lunar-induced tides passes through the local meridian at either 4:00 a.m. or 4:00 p.m. local time when the diurnal surface pressure is a minimum (this takes place roughly once every quarter of a synodic month = 7.38 days). In addition, if the generation of an EKW occurs at roughly the same time as the generation of an ERW (which takes place roughly once every quarter of a Tropical month = 6.83 days), the combined atmospheric waves reinforce the Westerly Wind Bursts (WWBs) that are produced by ERWs.

Further research is being carried out to test this modified hypothesis.

Thursday, February 7, 2019

The Lunar Tidal Model - Part 3

Please read:

The Lunar Tidal Model - Part 1
http://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-1.html

The Lunar Tidal Model - Part 2
https://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-2.html


The following question was presented in Part 2:

"Are the equatorial Rossby waves, that are seen trailing the active phase of an MJO, being generated at the times when there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator [when measured at the same time in the 24.8-hour lunar tidal day], either at a tidal minimum (i.e. at a lunar standstill) or at a tidal maximum (i.e. at a lunar equatorial crossing)?"

As a reminder, figure 1 [i.e. figure 2 in Part 2] below shows a schematic diagram of the relative (lunar-induced) tidal height on the Earth's equator, when measurements are taken at a fixed point in the 24.8-hour lunar tidal day. [Again, note that this is only a rough schematic diagram that is designed to give an idealistic view of how the tides would vary over a lunar tropical month. No attempt is made to allow for the varying distance of the Moon from the Earth and the actual values shown in the graph are only intended to create a qualitative impression of what is happening.]

Figure 1 starts out with the sub-lunar point at its northernmost latitude and it shows that there are four times during a tropical month where there is an ebb in the equatorial tidal height [when measured at a fixed point in the lunar day]. Each one corresponds to a lunar equatorial crossing or a lunar standstill.


Figure 1


The following refers to a specific case of an MJO event that occurred just recently between December 2nd of 2018 and January 6th of 2019. Figure 2 below shows lunar-induced changes in the the relative angular velocity (Delta Omega/Omega) of the Earth over this time period [Sidorenkov 2009]. This figure is used to identify six dates during this MJO event that are at, or within one day of, one of the times of either a lunar equatorial crossing or a lunar standstill. These dates are close to times when there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator [when measured at the same time in the 24.8-hour lunar tidal day].
  
Figure 2

The following set of six figures show surface wind patterns (1000 hPa level) in the Earth's atmosphere on the dates that are highlighted in figure 2 (https://earth.nullschool.net/). The wind maps cover the equatorial regions of the Indian and Western Pacific oceans. Each map shows the nominal location of the active phase of the MJO on the designated date [Note: This is only a rough estimate that is based upon the geological location of the published MJO phase for that date (Wheeler and Hendon 2004, BOM 2019)]. Additionally, each map shows the location of the Westerly Wind Bursts
(WWBs) and Equatorial Rossby Waves (ERW) associated with each MJO event. All six maps show surface wind conditions for the geological location of the active phase of the MJO at a time that corresponds to the local mid-afternoon













Some important points to note:

a) The MJO event stalls in phase 5 (located just south of the Philippines) between the December 15th, 2018 and January 1st, 2019. This could indicate that the propagation of this MJO wave was impeded by:
  • its passage through the Maritime Province (i.e. the Indonesian Archipelago)
  • its temporary linkage to the monsoon trough across the northern part of Australia.
b) The twin low-pressure cells that form on each side of the equator are a manifestation of the westerly propagating Equatorial Rossby Wave (ERW). These low-pressure cells only start forming a day or so before the dates of the six surface wind maps and so they appear to be associated with the ebb of the lunar-induced tides along the Earth's equator roughly once every 6.8 days.

c) The reemergence of a strong MJO event in phase region 7, following its passage through the Maritime Province, could be the result of the decoupling between the slower moving MJO wave and a much faster move Kelvin Wave that usually takes place in this region of the western Pacific Ocean.

Conclusion:

Careful analysis of these six maps supports the contention that the equatorial Rossby waves, that are seen trailing the active phase of an MJO, are being generated at the times when there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator [when measured at the same time in the 24.8-hour lunar tidal day], i.e. either at a tidal minimum (at a lunar standstill) or at a tidal maximum at the Earth's equator (at a lunar equatorial crossing).

N.B. This blog post is not a definite proof of the stated conclusion, however, it does provide evidence for further investigation of the proposed hypothesis.   

References:

Sidorenkov, N.S., 2009: The Interaction Between Earth’s Rotation and Geophysical Processes, Weinheim: Wiley.

https://earth.nullschool.net/ last accessed 07/02/2019

Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time multivariate MJO index:
Development of an index for monitoring and prediction. Mon. Wea. Rev.132, 1917-1932.

Australian Bureau of Meteorology (BOM), 2019: http://www.bom.gov.au/climate/mjo/  last accessed 06/02/2019.

Wednesday, February 6, 2019

The Lunar Tidal Model - Part 2

Please read:
The Lunar Tidal Model - Part 1
http://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-1.html

Introduction

Lian et al. 2014 [1] and Chen et al. 2015 [2] show that for every major El Nino event since 1964, the drop off in easterly trade wind strength at the start of these events has been preceded by a marked increase in westerly wind bursts (WWBs) in the western equatorial Pacific Ocean. These authors contend that the WWBs generate easterly moving equatorial surface currents which transport warm water from the warm pool region into the central Pacific. In addition, the WWBs create downwelling oceanic Kelvin waves in the western Pacific that propagate towards the eastern Pacific where they produce intense localized warming (McPhaden 1999 [3]). It is this warming that plays a crucial in the onset of El Nino events through its weakening of the westerly trade winds associated with the Walker circulation.

The WWBs are predominantly produced by twin low-pressure cells that straddle the Earth's equator in the western Pacific Ocean. Most of these low-pressure cell pairs are generated by westerly moving equatorial Rossby waves that are formed in the trailing edges of the active phase of the Madden Julian Oscillation (MJO).

Madden-Julian Oscillations (MJO)

Madden Julian Oscillations (MJOs) are the dominant form of intra-seasonal (30 to 90 days) atmospheric variability in the Earth’s equatorial regions ([4]). They are characterized by the eastward progression of a large region of enhanced convection and rainfall that is centered upon the Equator. 

This region of enhanced precipitation is followed by an equally large region of suppressed convection and rainfall. The precipitation pattern takes about 30 – 60 days to complete one cycle when seen from a given point along the equator ([5], [6]).

At the start of the enhanced convection phase of an MJO, a large region of greater than normal rainfall forms in the far western Indian Ocean and then propagates in an easterly direction along the equator. This region of enhanced rainfall travels at a speed of ~ 5 m/sec across the Indian Ocean, the Indonesian Archipelago (i.e. the Maritime Continent) and on into the western Pacific Ocean. However, once it reaches the central Pacific Ocean, it speeds up to ~ 15 m/sec and weakens as it moves out over the cooler ocean waters of the eastern Pacific.

An MJO consists of a large-scale coupling between the atmospheric circulation and atmospheric deep convection. When an MJO is at its strongest, between the western Indian and western Pacific Oceans, it exhibits characteristics that approximate those of a hybrid cross between a convectively-coupled Equatorial Kelvin Wave (EKW) and an Equatorial Rossby Wave (ERW, [7], [8], [9]).

MJOs are larger scale structures than either EKWs or ERWs. Figure 1 shows the hybrid structure of an MJO  that resembles a cross between a convectively-coupled EKW and an ERW.


Figure 1.


As with the EKWs, MJO's can spawn twin cyclones straddling the equator that can spin off and become tropical depressions. However, since MJO's are slower moving than EKWs, they tend to produce stronger and longer lasting WWBs than those produced by EKWs alone.

"There is strong year-to-year (interannual) variability in Madden–Julian oscillation activity, with long periods of strong activity followed by periods in which the oscillation is weak or absent."[10]

"This interannual variability of the MJO is partly linked to the El Niño-Southern Oscillation (ENSO) cycle. In the Pacific, strong MJO activity is often observed 6 – 12 months prior to the onset of an El Niño episode but is virtually absent during the maxima of some El Niño episodes,.."[10]



Possible Implications

In an earlier post:

https://astroclimateconnection.blogspot.com/2019/02/the-lunar-tidal-model-part-1.html

observational evidence was presented to show that El Ninos events must be initiated by a physical phenomenon that occurs at times when Perigean New/Full moons are either crossing the Earth's equator or reaching a lunar standstill. 

The one factor that occurs when New/Full moons either cross the Earth's equator or reach a lunar standstill is that the lunar-induced acceleration of the Earth's rotation changes sign. When this happens there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator, at each  tidal minimum (when the Moon is furthest from the Equator i.e at a lunar standstill) or tidal maximum (when the Moon is crossing the Earth's equator i.e. at a lunar equatorial crossing), provide measurements are taken at the same point in the 24.8-hour lunar tidal day [N.B. this effectively removes the diurnal variation of the lunar tides so that the long-term variations caused by the north-south movement of the Moon are evident over the tropical month].

Figure 2 shows a schematic diagram of the relative (lunar-induced) tidal height on the Earth's equator when measurements are taken at a fixed point in the 24.8-hour lunar tidal day. [Note that this is only a rough schematic diagram that is designed to give an idealistic view of how the tides would vary over a lunar tropical month. No attempt is made to allow for the varying distance of the Moon from the Earth and the actual values shown in the graph are only intended to create a qualitative impression.]

Figure 2 starts out with the sub-lunar point at its northernmost latitude and it shows that there are four times during a tropical month where there is an ebb in the equatorial tidal height [when measured at a fixed point in the lunar day]. Each one corresponds to a lunar equatorial crossing or a lunar standstill.

Figure 2



This leads us to ask the question: Are the equatorial Rossby waves that are seen trailing the active phase of an MJO being generated at the times where there is an ebb in the lunar-induced atmospheric/oceanic tides at the Earth's equator, either at a tidal minimum (i.e. at a lunar standstill) or at a tidal maximum (i.e. at a lunar equatorial crossing)?

This question will be further investigated in part 3.

References:

1. Lian, T., Chen D., Tang Y., and Wu Q. 2014, Effects of westerly wind bursts on El Niño:
A new perspective
, Geophys. Res. Lett., 41, 3522–3527, doi:10.1002/2014GL059989.

2. Chen D., Lian T., Fu C., Cane M.A., Tang Y., Murtugudde R., Song X., Wu Q., and Zhou L., 2015, Strong influence of westerly wind bursts on El Niño diversity, Nature Geoscience, Vol. 8 No 5, pp. 339 – 345, doi: 10.1038/NGEO2
399

3. McPhaden, M. J. (1999), Genesis and Evolution of the 1997-98 El Nino, Science, Vol 283, pp. 950 – 954.

4. Zhang, C. (2005), Madden-Julian Oscillation, Rev. Geophys., 43.

5. Madden R. and P. Julian, 1971: Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific, J. Atmos. Sci., 28, 702-708.

6. Madden R. and P. Julian, 1972: Description of global-scale circulation cells in the tropics with a 40-50 day period. J. Atmos. Sci., 29, 1109-1123.

7. Masunaga, H. Seasonality and Regionality of the Madden-Julian Oscillation, Kelvin Wave, and Equatorial Rossby Wave. J. Atmos. Sci., Vol. 64, pp. 4400-4416, 2007

8. Kang, In-Sik; Liu, Fei; Ahn, Min-Seop; Yang, Young-Min; Wang, Bin., 2013, The Role of SST Structure in Convectively Coupled Kelvin-Rossby Waves and Its Implications for MJO Formation, Journal of Climate, vol. 26, issue 16, pp. 5915-5930.


10. https://en.wikipedia.org/wiki/Madden-Julian_oscillation